MinT - Best Known (82−71, 82, s)-Nets in Base 64

Best Known (82−71, 82, s)-Nets in Base 64

(82−71, 82, 177)-Net over F₆₄ — Constructive and digital

Digital (11, 82, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 82, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(82−71, 82, 225)-Net over F₆₄ — Digital

Digital (11, 82, 225)-net over F₆₄, using

t-expansion [i] based on digital (10, 82, 225)-net over F₆₄, using
- net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(82−71, 82, 3323)-Net in Base 64 — Upper bound on s

There is no (11, 82, 3324)-net in base 64, because

1 times m-reduction [i] would yield (11, 81, 3324)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 199 897860 961721 950942 746986 588622 842791 254081 746234 483608 161434 502941 155569 682328 406143 129105 039013 996171 720392 782605 915718 466454 623883 335794 529635 > 64⁸¹ [i]